Michal Eckstein
Asymptotic expansions of heat traces have multifarious applications both in pure mathematics (e.g. index theorems) as well as in mathematical physics (e.g. QFT). Drawing from the theory of general Dirichlet series, I will explain the interplay between heat traces and spectral zeta functions in full generality of operators on a Hilbert space. I will establish general conditions under which an asymptotic expansion of the heat trace exists and discuss its convergence. The general theory will be illustrated with a number of geometrically motivated examples.
